Social Status is a Matter of Circumstance

All things being equal, I do not think a person's status matters much in whether or not you have a close relationship with them. However, we do not live in that kind of world.

Two strangers -- one rich and one poor -- could, let's say, get stuck in an elevator together and become fast friends while waiting to be rescued. However, once they leave the elevator, the circumstances of their social status will begin to affect their relationship.

If the two of them left on a casual "see you around" note, they will probably not see each other again. How often is the poor person going to be shopping at Henri Bendel or eating at Nobu? How often is the rich person going to be at their local check-cashing place or eating at Taco Bell?

If they exchanged contact info back in that elevator, perhaps they will hang out once or twice, but where could they go? The poor person will not be able to afford the luxuries of the rich person and the rich person may eventually resent having to pay for everything or having to "slum" it all the time. The bond would have to be really strong -- namely, a familial or a romantic relationship -- to overcome that.

Simple -- friendship is much harder to maintain, I think, when faced with such a divide. A social status has its own bubble -- even beyond what you can afford and the places you go, but in where you live, how you dress, and even in some cases, how you speak. It is easiest to be friends with someone nearly or completely within your own bubble.

The only way around it (besides it being a familial or romantic relationship), I think, is if you have a connection that does not involve status; a place where wealth does not factor into it at all -- like if you both attend the same classes or if you are both in a group like Alcoholics Anonymous. A long-standing connection may be able to overcome a wide disparity in status. The real test would be if those people could maintain the friendship after the connection is gone.